Chapter D. Latitudes and Departures - 3. Examples

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3. Examples

In the following examples shown, all calculations are shown with an additional significant figure. Because these are generally intermediate computations, carrying an additional digit minimizes roundoff error in subsequent calculations.

When reporting results of an intermediate calculation, those should be stated to the correct number of significant figures so as not to imply an accuracy beyond that of the measurements.

a. Traverse with bearings

Equation D-6

Lat and Dep will always compute as positive; must assign correct mathematical sign based on the bearing quadrant.

Figure D-10 Bearing Traverse

Line AB

Because the bearing is South and West, the Lat and Dep are -176.357' and -438.548' respectively.

Line BC

Because the bearing is North and West, the Lat and Dep are +203.395' and -73.093' respectively.

Line CD

Because the bearing is North and East, the Lat and Dep are +192.357' and +198.651' respectively.

Line DA

Because the bearing is South and East , the Lat and Dep are -219.312' and +313.065' respectively

In tabular form:

Line

Bearing

Length (ft)

Lat (ft)

Dep (ft)

AB

S 68°05'35"W

472.68

-176.357

-438.548

BC

N 19°46'00"W

216.13

+203.395

-73.093

CD

N 45°55'20"E

276.52

+192.357

+198.651

DA

S 54°59'15"E

382.24

-219.312

+313.065

sums:

1347.57

+0.083

+0.075

Distance

Lat err

Dep err

too far N

too far E

b. Traverse with azimuths

Equation D-7

Lat and Dep will always compute directly with the correct sign when using azimuths.

Figure D-11 Azimuth Traverse

Line ST

Line TU

Line UV

Line VS

Line

Azimuth

Length (ft)

Lat (ft)

Dep (ft)

ST

309°05'38"

347.00

+218.816

-269.311

TU

258°34'22"

364.55

-72.226

-357.324

UV

128°04'44"

472.74

-291.560

+372.123

VS

60°21'26"

292.94

+144.885

+254.602

sums:

1477.23

-0.085

+0.090

Distance

Lat err

Dep err

too far S

too far E

c. Crossing Traverse

A four-sided parcel has two obstructed lines.

Figure D-12 Parcel Boundaries

In order to create a closed traverse, the survey crew measures a crossing traverse which connects all four points.

As long as a traverse closes back on its beginning point, the closer condition is still:

regardless of how many times it may cross itself.

Given this traverse data, determine its closure and precision.

Figure D-13 Closed Crossing Traverse

Rather than write out each Lat and Dep computation separately, we can simply set up the table and record the computations in it.